The present work also has important implications on the high temperature superconductivity in the single-layer FeSe/SrTiO\(_3\)  films. First, our results indicate that the electron-pocket-near-M-only Fermi surface topology is not confined to the superconducting single-layer FeSe/SrTiO\(_3\)  films only; instead, it can also be present in bulk superconductors. Our experimental results have shown that this form of Fermi surface topology is favorable for achieving high temperature superconductivity in the iron-based superconductors. Second, it is remarkable that T\(_c\)  as high as 41 K can be achieved in the bulk FeSe11111 superconductor where there is no strain effect, no interface effect, and no strong electron-phonon coupling effect[1]} involved as in the superconducting single-layer FeSe/SrTiO\(_3\)  films. It is known from the superconducting single-layer FeSe/SrTiO\(_3\)  films that T\(_c\)  can be tuned by varying the electron doping level[2]}. Therefore, it is possible that T\(_c\) =41 K is lower in FeSe11111 than that in the superconducting single-layer FeSe films (\(\sim \) 65 K or higher) because the electron doping level in FeSe11111 is low. This raises a big possibility that T\(_c\)  of the FeSe11111 superconductor may be further increased if higher electron-doping is made possible and the superconductor-insulator transition[3]} can be avoided. The high T\(_c\)  and its possible enhancement with increasing doping in the FeSe11111 superconductor provide key insight on understanding the superconductivity in the single-layer FeSe/SrTiO\(_3\)  films. Third, we note that the in-plane lattice constant a or b of the FeSe11111 superconductor (3.78 \(Å\) )[4]}, [5]} is comparable to the primary bulk FeSe superconductor (3.76 \(Å\) ), but significantly smaller than the single-layer FeSe film epitaxially grown on the SrTiO\(_3\)  substrate (3.905 \(Å\) ). Considering high T\(_c\) =41 K and its possible enhancement upon further elecron-doping in the FeSe11111 superconductor, this indicates that the interface strain does not play primary role in determining T\(_c\) . On the other hand, the distance between the two adjacent FeSe layers seems to have strong correlation with superconductivity in the FeSe-based superconductors. As the distance changes from 5.5 \(Å\)  for bulk FeSe, to 9.32 \(Å\)  in the FeSe11111 superconductor, and to infinity in the single-layer FeSe/SrTiO\(_3\)  films, T\(_c\)  increases from 8.5 K, to 41 K, to 65 K or higher (Fig. 1). In the meantime, the top of the hole-like band at \(\Gamma \)  changes its position from above the Fermi level for bulk FeSe[6]}, to 50\(\sim \) 70 meV below the Fermi level for FeSe11111, to 80 meV below the Fermi level for the superconducting single-layer FeSe films (Fig. 2). These results again indicate that suppression of the hole-like bands near the \(\Gamma \)  point is favorable for achieving high temperature superconductivity in the iron-based superconductors.
